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Casino War

Introduction

Casino War is without a doubt the easiest card game to play in the casino. If you have ever played war as a child, or simply made a bet on who could draw the highest card, then war will seem instantly familiar. Following are the specific rules.

Rules

The game is played with six decks. Cards are ranked as in poker, except aces are always high. The suit does not matter.

After the players have made a wager each player and the dealer shall get one card.

Each player's card shall be compared with the dealer's card. If the player's card is higher he wins even money. If the dealer's card is higher the player loses.

In the event of a tie the player shall have two choices: (1) surrender and forfeit half the bet or (2) go to war (see rule 5)

If the player elects to go to war he must raise his bet by an amount equal to his original wager. The dealer will do the same but this is just for show. The dealer will then burn three cards and give the player and dealer another card each. If the player's second card equals or beats the dealer then the player shall win even money on the raise only and the original wager shall push. If the dealer's second card is greater the player shall lose both bets.

At some casinos, the Mirage and Casino Niagara to name just two, a tie after a tie will result in a bonus equal to the original wager. At the Casino Niagara they say the raise pays 3 to 1 but the initial bet loses, which is mathematically the same thing.

A tie bet is also available, which pays 10 to 1 if the first two cards tie.

I'm often asked where the house edge lays in this game. Where the edge comes from is when there is a war you either win one unit or lose two. For example, if you originally bet $5 you have to double your bet, risking $10, to win only $5.

Analysis

Stingy Rules

The following table shows the possible outcomes in a six-deck game with no bonus for a tie after a tie, assuming the player always goes to war.

Six Decks — Stingy Rules

Event

Pays

Probability

Return

Win

1

0.502735

0.502735

Lose original bet

-1

0.463023

-0.463023

Lose after war

-2

0.034242

-0.068484

Total

1.000000

-0.028771

The standard deviation under these rules is 1.049714.

Liberal Rules

The next table shows the possible outcomes in a six-deck game with a bonus equal to the Ante for a tie after a tie, assuming the player always goes to war.

Six Decks — Liberal Rules

Event

Pays

Probability

Return

Win with tie after tie

2

0.005471

0.010942

All other wins

1

0.497265

0.497265

Lose original bet

-1

0.463023

-0.463023

Lose after war

-2

0.034242

-0.068484

Total

1.000000

-0.023301

The standard deviation under these rules is 1.057637.

Super Liberal Rules

Internet casinos using Gamesys software feature a rule where the player gets a bonus of 3x the Ante bet if the player gets a tie after a tie. The following table shows this lowers the house edge to 1.24%.

Six Decks — Super Liberal Rules

Event

Pays

Probability

Return

Win with tie after tie

4

0.005471

0.021884

All other wins

1

0.497265

0.497265

Lose original bet

-1

0.463023

-0.463023

Lose after war

-2

0.034242

-0.068484

Total

1.000000

-0.012358

Some Interent casinos use unusual number of decks. The following table shows the house edge under the bonus rules, normal "no bonus" rules, surrendering on ties, and the tie bet itself.

Casino War House Edge

Decks

With Bonus

No Bonus

Surrender

Tie

1

2.06%

2.42%

2.94%

35.29%

2

2.24%

2.70%

3.40%

25.24%

3

2.29%

2.79%

3.55%

21.94%

4

2.31%

2.84%

3.62%

20.29%

5

2.32%

2.86%

3.67%

19.31%

6

2.33%

2.88%

3.70%

18.65%

7

2.34%

2.89%

3.72%

18.18%

8

2.34%

2.90%

3.73%

17.83%

Tie Analysis

The following table shows the probability of winning and expected return on the Tie bet, assuming it pays the usual 10 to 1.